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Opus in profectus

# Pressure

## Discussion

### definition

Pressure is the ratio of force applied to the area covered…

 P = F A

The unit of pressure is the pascal

 ⎡⎢⎣ Pa = N = kg m/s2 = kg ⎤⎥⎦ m2 m2 m s2

The pascal is also a unit of stress and the topics of pressure and stress are connected.

• Bed of nails (not really pressure but shear strain, which has the same units)
• Finger bones are flat on the gripping side to increase surface area in contact and thus reduce compressional stresses

### gauge vs. absolute

Selected gauge pressures (black‑positive, red‑negative)
atm kPa device, event, phenomenon, process
200 20,000 pressurized breathing apparatus
140 14,000 milk homogenization
110 11,000 rupture compression strength of vertebral disks
7–14 700–1400 puffed cereal manufacture
9 900 espresso machine
4–7 400–700 bicycle tire
>4 >400 oxygen poisoning and nitrogen narcosis for dives > 30 m
2.7–4.1 275–415 champagne at serving temperature (10 °C)
2.7 275 carbonated soft drinks
2.0–2.5 200–250 car tire
>4 >400 blast wave, 100% lethality
2.3–4.0 230–400 blast wave, 50% lethality
1.6–2.3 160–230 blast wave, 1% lethality
1.02 103 typical household pressure cooker
1 101.325 one standard atmosphere over environment
47 bottom of feet while standing
20 lungs, extreme exhalation
17 sustained pressure, eardrum ruptures
8 sustained pressure, eardrum senses pain
13–19 blood pressure, arterial, systolic (during a heartbeat)
8–12 blood pressure, arterial, diastolic (between heartbeats)
7–14 aircraft shock wave
11 eye, severe glaucoma
1.6–3.0 eye, normal
7 tennis ball
4.0 blood pressure, capillary, arterial end
1.3 blood pressure, capillary, venous end
3 bladder, micturition reflex (gotta go urge)
1.3–2.6 gastrointestinal tract
0.6–1.6 cerebrospinal fluid
0.4–0.9 blood pressure, venous
0.6–0.8 interstitial fluid (osmotic pressure)
2 acoustic pressure, eardrum ruptures (160 dB)
0.02 acoustic pressure, eardrum senses pain (120 dB)
2 × 10−8 acoustic pressure, threshold of hearing (0 dB)
0 0 environmental pressure
−1.3 lungs, resting
−1.5 lungs, drinking through a 15 cm straw
−25 lungs, extreme inhalation
−1 −101.325 one standard atmosphere below environment, a perfect vacuum in a standard atmosphere
Selected absolute pressures (largest to smallest)
atm Pa device, event, phenomenon, process
3.4 × 1011 3.4 × 1016 center of the Sun
???? ???? center of Jupiter
1010 1015 diamond anvil, record high
3.6 × 106 3.6 × 1011 center of Earth
1,080 1.1 × 108 Marianas Trench, Pacific Ocean (−10,924 m)
160 1.6 × 107 Lake Baikal, Asia (−1,620 m)
140 1.4 × 107 Lake Tanganyika, Africa (−1,470 m)
90 9.0 × 106 surface of Venus
40 4.0 × 106 Lake Superior, North America (−406 m)
???? ???? record dive by a human
26 2.6 × 106 helium freezes at about 1 K
>3 >300,000 oxygen poisoning and nitrogen narcosis for dives > 30 m
108,380 Earth atmosphere, record high, altitude adjusted (Siberia, 1968)
106,000 Earth atmosphere, Dead Sea (−400 m)
1 101,325 Earth atmosphere, sea level, standard atmosphere
90,000 Earth atmosphere at 1,000 m, interior of Concorde
87,000 Earth atmosphere, record low, altitude adjusted (Typhoon Tip, 1979)
80,000 Earth atmosphere at 2,000 m, interior of commercial jet aircraft
65,000 Earth atmosphere, La Paz, Bolivia (3,650 m)
53,000 Earth atmosphere, highest permanently inhabited town (5,100 m)
~40,000~ Earth atmosphere, vertical limit of human survivability (~7,000 m)
~⅓ 31,000 Earth atmosphere, Mount Everest (8,848 m)
~⅕ 19,000 Earth atmosphere, altitude of commercial jet aircraft (12,000 m)
0.063 6,400 Earth atmosphere, Armstrong limit, exposed body liquids boil (19,000 m)
>0.033  >3,300> low vacuum (LV)
<0.033  <3,300< medium vacuum (MV)
0.025 2,200 Earth atmosphere, altitude of reconnaissance plane (26,000 m)
0.007 700 surface of Mars
0.002 230 Earth atmosphere, altitude of highest sky dive (41,422 m)
0.0006 60 Earth atmosphere, altitude of highest unmanned balloon flight (52,000 m)
~10−5 ~1 surface of Pluto, maximum
<10−6 <0.1 high vacuum (HV)
<10−9 <10−4 very high vacuum (VHV)
<10−12 <10−7 ultra high vacuum (UHV)
~10−13 ~10−8 surface of the Moon, daytime
~10−15 ~10−10 surface of the Moon, nighttime
<10−15 <10−10 extreme ultrahigh vacuum (XHV)
~10−17 ~10−12 I am told that below this value all vacuum equipment leaks

### the atmosphere

Standard Atmospheric Tables

Chemical composition of the atmosphere Source: US Standard Atmosphere, 1976
gas formula molecular
weight (g/mol)
fraction
nitrogen N2 028.0134000 0.780840000
oxygen O2 031.9988000 0.209476000
argon Ar 039.9480000 0.009340000
carbon dioxide CO2 044.0099500 0.000314000
neon Ne 020.1830000 0.000018180
helium He 004.0026000 0.000005240
methane CH4 016.0430300 0.000002000
krypton Kr 083.8000000 0.000001140
hydrogen H2 002.0159400 0.000000500
xenon Xe 131.3000000 0.000000087
overall 028.9644253 0.999997147

### fluids

The gauge pressure in a uniform fluid at a particular depth is directly proportional to…

• the density of the fluid (ρ). The denser the fluid, the greater the pressure.
• the acceleration due to gravity (g). The stronger the gravity, the greater the pressure.
• the depth (h). The deeper you go, the greater the pressure.

Combining these factors gives the gauge pressure (Pg) at any depth…

Pg = ρgh

Adding on the the surface pressure (P0) gives the absolute pressure…

P = P0 + ρgh

The absolute pressure in a uniform or nonuniform fluid at a particular depth (h) measured along the vertical axis (z) is given by…

 h P = P0 + ⌠⌡ ρ(z)g(z) dz 0

Pressure in a uniform fluid — Stevin's law. Simon Stevin (1548–1620) discovered the hydrostatic paradox that the downward pressure of a liquid is independent of the shape of the vessel, and depends only on its height. Stevin was probably the first to work with the concept of pressure, having lived entirely before Pascal or Bernoulli. Stevin's Flemish word for pressure was the noun gheprang from the verb pranghen, to press (geprang and prangen in modern spelling). The current Dutch word for pressure is druk and the verb to press is drukken.

### devices

barometer

barometer, manometer, Hare's apparatus

The atmosphere as a unit.

 1 atm = 101,325 Pa (by definition) = 760 torr (by definition) = 763.43… mm Hg (approximately) = 1.03… kg/cm2 (approximately) = 10.3… tonnes/m2 (approximately) = 14.7… psi (approximately) = 1.06… tons/ft2 (approximately)

### physiology

blood pressure

ear pressure in the middle ear: eardrum at end of outer ear connected to smaller oval window at beginning of inner ear. 15-30 times greater pressure. combination of difference in membrane diameters and lever effects of middle ear bones.

eye pressure and glaucoma

Circulatory pressures (mm Hg, a.k.a. torr) Source: Physics of the Body (paid link)
location systolic diastolic mean
aorta 120 80 100
left ventricle 120 8
left atrium 7 10 4
pulmonay artery 15 7 12
right ventricle 15 2
right atrium 4 4 0
pulmonary capillary wedge 7 10 4

### pascal's principle

• Pascal's principle: Pressure changes applied to the surface of an enclosed fluid are transmitted evenly throughout the fluid.
• Water seeks its own level. That's one of the realities of life.
• hydraulics
• Queckenstedt's maneuver - barbaric medical test from the early 20th century to test for spinal stenosis